Vinay Deolalikar, who works at the research arm of Hewlett-Packard in Palo Alto, California, believes he has solved the riddle of P vs NP in a move that could transform mankind’s use of computers as well as earn him a $1m (£650,000) prize.

P vs NP is one of the seven millennium problems set out by the Massachusetts-based Clay Mathematical Institute as being the “most difficult” to solve.

Many mathematical calculations involve checking such a large number of possible solutions that they are beyond the current capability of any computer. However, the answers to some are quick and easy to verify as correct. P vs NP considers if there is a way of arriving at the answers to the calculations more quickly in the first place.

Mr Deolalikar claims to have proven that P, which refers to problems whose solutions are easy to find and verify, is not the same as NP, which refers to problems whose solutions are almost impossible to find but easy to verify.

His paper, posted online on Friday, is now being peer-reviewed by computer scientists.

Scott Aaronson, associate professor of computer science at the Massachusetts Institute of Technology, is so sceptical that he pledged on his blog to pay Mr Deolalikar an additional $200,000 (£125,000) if the solution is accepted by Clay.